This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the inverse of a 2 × 2 matrix A = a & b \\ c & d , the formula is: A^-1 = (1)/(ad - bc) d & -b \\ -c & a Step 1: Identify the elements of matrix A. Given A = 2 & 1 \\ 5 & 3 , we have a=2, b=1, c=5, and d=3. Step 2: Calculate the determinant of A. The determinant is ad - bc. (A) = (2)(3) - (1)(5) = 6 - 5 = 1 Step 3: Apply the inverse formula. Substitute the values into the formula. A^-1 = (1)/(1) 3 & -1 \\ -5 & 2 A^-1 = 3 & -1 \\ -5 & 2 Comparing this result with the given options, the correct answer is the fourth option. The final answer is 3 & -1 \\ -5 & 2 . That's 2 down. 3 left today — send the next one.